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Weak Differentiability with Applications to Variational Analysis

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Abstract

In this paper we first review the theory of weak differentiability with some improvements and unifications of existing results; then we introduce an extended variant of this notion and establish its basic properties; finally we use the weak differentiability and its variant to develop new calculus results in variational analysis for the theory of generalized differentiation and the sequential normal compactness. In this way we demonstrate that the weak differentiability and its variant, in contrast to the usual differentiability, are in fact more suitable for Fréchet and limiting/Mordukhovich constructions in variational analysis.

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Authors and Affiliations

  1. Department of Mathematics, Eastern Michigan University, Ypsilanti, MI, 48197, USA

    Bingwu Wang

  2. Department of Mathematics, Chongqing Normal University, Chongqing, 400047, People’s Republic of China

    Xinmin Yang

Authors
  1. Bingwu Wang
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  2. Xinmin Yang
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Correspondence to Bingwu Wang.

Additional information

The work of the second author was partially supported by the National Science Foundation of China (Grant No. 11431004).

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Wang, B., Yang, X. Weak Differentiability with Applications to Variational Analysis. Set-Valued Var. Anal 24, 299–321 (2016). https://doi.org/10.1007/s11228-015-0341-8

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  • DOI: https://doi.org/10.1007/s11228-015-0341-8

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